Singularities of parallel manipulators: a geometric treatment
Singularities of parallel manipulators: a geometric treatment
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DOI：
10.1109/tra.2003.814507
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发表时间：
2003-08
期刊：
影响因子：
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通讯作者：
Guanfeng Liu;Y. Lou;Zexiang Li
中科院分区：
文献类型：
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作者：
Guanfeng Liu;Y. Lou;Zexiang Li
并联机器人自然地与由其闭合约束定义的一组约束函数相关联。这些约束函数的微分形式完全刻画了机械手的几何特性。在本文中，使用微分形式的语言，我们提供了一个彻底的几何研究的各种类型的奇异的并联机器人，它们的关系与运动参数和配置空间的机械手，和作用冗余驱动在重塑奇异和提高性能的机械手。首先，我们通过在一些适当定义的空间上构造莫尔斯函数来分析位形空间的奇异性。通过改变机械臂的关键参数，我们得到了位形空间的同伦类。这使我们能够深入了解配置空间的奇异性，并了解如何选择设计参数的机械手。其次，我们定义了参数化奇点，其中包括执行器和末端执行器奇点（或其他等效定义）作为其特殊情况。这个定义自然包含的封闭约束，除了坐标的致动器和末端执行器，可以用来搜索一组完整的致动器或末端执行器的奇点，包括一些奇点，可能会错过了通常的运动学方法。我们给出了参数化奇点的一个内禀分类，并定义了它们的拓扑序。虽然非退化奇点一般不会造成问题，但退化奇点有时可能是危险的来源，应该尽可能避免。
A parallel manipulator is naturally associated with a set of constraint functions defined by its closure constraints. The differential forms arising from these constraint functions completely characterize the geometric properties of the manipulator. In this paper, using the language of differential forms, we provide a thorough geometric study on the various types of singularities of a parallel manipulator, their relations with the kinematic parameters and the configuration spaces of the manipulator, and the role redundant actuation plays in reshaping the singularities and improving the performance of the manipulator. First, we analyze configuration space singularities by constructing a Morse function on some appropriately defined spaces. By varying key parameters of the manipulator, we obtain homotopic classes of the configuration spaces. This allows us to gain insight on configuration space singularities and understand how to choose design parameters for the manipulator. Second, we define parametrization singularities which include actuator and end-effector singularities (or other equivalent definitions) as their special cases. This definition naturally contains the closure constraints in addition to the coordinates of the actuators and the end-effector and can be used to search a complete set of actuator or end-effector singularities including some singularities that may be missed by the usual kinematics methods. We give an intrinsic classification of parametrization singularities and define their topological orders. While a nondegenerate singularity poses no problems in general, a degenerate singularity can sometimes be a source of danger and should be avoided if possible.